Recursive & Explicit Sequences

Front

What is a recursive sequence?

Back

A sequence where each term is defined based on one or more previous terms.

Front

What is an explicit formula?

Back

A formula that allows you to calculate the nth term of a sequence without needing to know the previous terms.

Front

What is the common difference in an arithmetic sequence?

Back

The constant amount that each term increases or decreases by.

Front

How do you find the nth term of an arithmetic sequence?

Back

Use the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The factor by which each term is multiplied to get the next term.

Front

How do you identify a recursive formula?

Back

It typically has the form a_n = f(a_{n-1}), where f is a function of the previous term.

Front

What is the first term of the sequence defined by a_n = -3n + 50?

Back

47, when n=1.

Front

What is the 15th term of the sequence a_n = -3n + 50?

Back

5.

Front

What is the recursive rule for the sequence 11, 22, 44, 88?

Back

a_n = 2a_{n-1}.